Cross

One imagination puzzle.

Can you cut and reassemble a square so that you create a red cross of the same volume?

(A cross is made of 5 identical squares)

Hint

The solution is quite elegant.

If you are a mathematical type calculate how high the cross will be and how you can create this height.

Answer

I hope the picture is quite illustrating.

Another solutions exist this seems most elegant to me though. If you have a different one you can easily check if it is correct yourself.